Simplify (54x^0y^5)/(9x^3y)

$\frac{54 x^{0} y^{5}}{9 x^{3} y}$

Step 1

Move $x^{0}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{54 y^{5}}{9 x^{3} y x^{0}}$

Step 2

Multiply $x^{3}$ by $x^{0}$ by adding the exponents.

Move $x^{0}$ .

$\frac{54 y^{5}}{9 (x^{0} x^{3}) y}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{54 y^{5}}{9 x^{0 + 3} y}$

Add $0$ and $3$ .

$\frac{54 y^{5}}{9 x^{3} y}$

Step 3

Cancel the common factor of $54$ and $9$ .

Factor $9$ out of $54 y^{5}$ .

$\frac{9 (6 y^{5})}{9 x^{3} y}$

Cancel the common factors.

Factor $9$ out of $9 x^{3} y$ .

$\frac{9 (6 y^{5})}{9 (x^{3} y)}$

Cancel the common factor.

$\frac{9 (6 y^{5})}{9 (x^{3} y)}$

Rewrite the expression.

$\frac{6 y^{5}}{x^{3} y}$

Step 4

Cancel the common factor of $y^{5}$ and $y$ .

Factor $y$ out of $6 y^{5}$ .

$\frac{y (6 y^{4})}{x^{3} y}$

Cancel the common factors.

Factor $y$ out of $x^{3} y$ .

$\frac{y (6 y^{4})}{y x^{3}}$

Cancel the common factor.

$\frac{y (6 y^{4})}{y x^{3}}$

Rewrite the expression.

$\frac{6 y^{4}}{x^{3}}$